# -*- coding: utf-8 -*-
"""
Spyder Editor

This is a temporary script file.
"""
a,b=105,24

while b > 0:
    a, b = b, a % b
print(a)

c,d=6024,1284

while d > 0:
    c, d = d, c % d
print(c)

e,f=98777,12945

while f > 0:
    e, f = f, e % f
print(e)

x,xprev,y,yprev=0,1,1,0
g,h=105,24
'''put in any positive integers for g and h with g>h'''
while h > 0:
    q=float(g//h)
    g, h = h, g % h
    x, xprev = xprev - q * x, x
    y, yprev = yprev - q * y, y
print(g,xprev,yprev)

'''2C part(1)'''
a,b=105,24
'''put in any positive integers for a and b with a>b'''
z=0
while b > 0:
    a, b = b, a % b
    z=z+1
print(a,z)
#the z output is the number of steps in the euclid algorithm

#2C part(2)-(5)
from math import log
from math import pi
from math import e
a,b=317811,196418
'''put in any positive integers for a and b with a>b'''
z=0
maximum_z=5*log(a,10)
average_z=(12/pi**2)*log(2,e)*log(a,e)
while b > 0:
    a, b = b, a % b
    z=z+1
print(z,maximum_z,average_z)
'''a=105 and b=16 gives z=5 and z_aprrox=3.9221991448330873, this is an
example the number of steps in the euclid algorithm being larger than the
average. a=105 and b=21 gives z=1 and z_approx=3.9221991448330873, this
is an example of the nuber of steps in the euclid algorithm being
lower than the average number of steps.
if you set a and b equal to the fibonacci numbers 317811 and 196418
respectively, we get z = 26 and 27.51084462415267  '''